gwenspooner85

Hi there, I'd like to help but can you please show the figures. It's easy, just take a screenshot, and select the "Image" button here in the text box and upload it. Thanks!

Create an equation and solve.

\(2x+10=\frac{1}{2}(5x+30)\\ 2x+10=\frac{5x+30}{2}\\ 4x+20=5x+30\\ x=-10\)

1. The answer is 2010 because finding the inverse is finding the f(x) that results in 2010 when plugged into x^2+3x^2+3x+1. When we get the inverse, we then have f(inverse), which is plugging it straight back into x^2+3x^2+3x+1. Then the result is the same.

2. f(f(1)

=f(1/1+2)

=f(1/3)

=1/(1/3+2)

=1/7/3

=3/7

9x-4y=30, 7x+y=11. 

We convert these to y-intercept form first.

9x-4y=30

4y=9x-30

y=9/4x-30/4

7x+y=11

y=-7x+11

Then set them equal to each other.

9/4x-30/4=-7x+11

37/4x=74/4

x=2

Then y=-3.

Therefore the point of intersection is (2, -3).

\(\frac{4x}{x^2-8x+15}=\frac{A}{x-3}+\frac{B}{x-5}\\ \frac{4x}{x^2-8x+15}=\frac{A(x-5)}{x^2-8x+15}+\frac{B(x-3)}{x^2-8x+15}\\ 4x=A(x-5)+B(x-3)\\ 4x=Ax-5A+Bx-3B\\\)

The x terms, Ax and Bx must add up to 4x so A+B=4. The constant terms, -5a and -3B must add up to 0 so -5A-3B=0.

We have a system of equations:

A+B=4

-5A-3B=0

Solving, we get A= -6 and B=10.

You're welcome. :)

The current average is 9+13+15+17+19+23+31+49\8=22. The current median is 9, 13, 15, 17 | 19, 23, 31, 49: 18.

The average increases by 2 so the new average after removing two numbers is 24. The median increases by 2 as well so the new median is 20.

After removing 2 numbers, we have 6 left. The remaining 6 numbers must add up to 24*6=144. 

176-144=32 is the sum of the two numbers removed.  The two numbers removed could be 9, 23; 13, 19; or 15,17. Using guess and check, 13 & 19 satisfy this.

Their product is 247.

We let x be the cost of a brownie and y the cost of a cookie.

Alvin pays 4x+3y. Milly pays 2x+16y.

Since Milly pays twice as much as Alvin we form an equation.

2(4x+3y)=2x+16y

8x+6y=2x+16y

6x=10y

x=5/3y

So a brownie is 5/3 times as expensive as a cookie.

You're welcome.

x^2-y^2 is the difference of squares: (x+y)(x-y)

So (x+y)(x-y)=63

We already know x-y=3.

3(x+y)=63

x+y=21

We can form a system of equations from this.

x-y=3

x+y=21

We solve and find that x=12 and y=9.

So x^2+y^2=12^2+9^2=144+81=225.